Vargas (3-0) struck out nine, one shy of his career high, walked none and allowed four hits in seven innings. He was removed after 92 pitches, 61 of them strikes.
Vargas, who missed most of last season after 2015 Tommy John surgery, lowered his ERA to 0.44.
Bumgarner, who went 2-0 plus a five-inning save in Game 7 of the 2014 World Series against the Royals, allowed one run and seven hits while walking one and striking out four in six innings.
Bumgarner (0-3) is still looking for his first victory this season after four starts, but for the third straight start he has been supported with one or no runs.
After Vargas' departure, Joakim Soria worked a spotless eighth and has yet to give up a run in eight innings this season.
Kelvin Herrera worked around a leadoff walk in the ninth to collect his third save in four opportunities.
The Royals closed out the homestand with five victories in six games to even their record at 7-7.
The Royals got their second run in the eighth off reliever George Kontos. Eric Hosmer sliced an opposite-field double with one out and scored on Salvador Perez's single.
The Royals managed to score a run off Bumgarner in the fifth. Paulo Orlando's ground-ball single to left with one out started it. Orlando on a delayed steal swiped second. The Giants challenged the ruling, but after a 2:16 delay, the call on the field stayed.
Orlando took third on Alex Gordon's groundout. He scored on Mike Moustakas' infield single to first baseman Brandon Belt, who knocked the ball down. Bumgarner was late in covering first, allowing Moustakas to beat the throw and get Orlando home.
The Royals had a chance to pad their lead after Lorenzo Cain drilled a double into the left-field corner with Moustakas stopping at third. Hosmer flied out to shallow left to strand the runners.
The Royals' struggles with runners in scoring position continued early. They went 0-for-3 with runners-in-scoring-postion in the second and third innings after going 1-for-11 in the loss Tuesday.
Gordon and Moustakas singled with one out in the third off Bumgarner, only the second and third hits he has yielded this season to left-handed hitters. Bumgarner stranded them on Cain and Hosmer groundouts.
Cheslor Cuthbert scolded a ball that third baseman Eduardo Nunez caught to end the second with Whit Merrifield on third and Alcides Escobar, who had doubled, on second.
Vargas retired the first 10 Giants he faced, striking out six, before giving up a fourth-inning single to Belt, who stopped at second on Buster Posey's two-out single. Brandon Crawford popped up to Escobar to end the inning.
NOTES: Aaron Hill made his second career start in left field. He has also started two at second base and one at third base this season for the Giants. ... 2B Raul Mondesi, who is hitting .114, was not in the lineup against Giants LHP Madison Bumgarner. Whit Merrifield replaced him at second. ... Cheslor Cuthbert was the Royals DH for the second time this season, although he is in an 0-for-13 skid. ... The Royals will open a four-game series Thursday at Texas. Royals LHP Danny Duffy and Rangers RHP Andrew Cashner are the pitching probables. ... The Giants are off Thursday before a weekend series at Colorado. Manager Bruce Bochy, who underwent an ablation procedure Tuesday, is scheduled to rejoin the club Friday after missing the two Kansas City games.